Graphics.Rasterific.CubicBezier:cachedBezierAt from Rasterific-0.6.1

Percentage Accurate: 92.5% → 96.5%

Time: 10.7s

Alternatives: 16

Speedup: 0.9×

• 31.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (+ (+ (+ x (* y z)) (* t a)) (* (* a z) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return ((x + (y * z)) + (t * a)) + ((a * z) * b);
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = ((x + (y * z)) + (t * a)) + ((a * z) * b)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return ((x + (y * z)) + (t * a)) + ((a * z) * b);
}

Python

def code(x, y, z, t, a, b):
	return ((x + (y * z)) + (t * a)) + ((a * z) * b)

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(Float64(x + Float64(y * z)) + Float64(t * a)) + Float64(Float64(a * z) * b))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = ((x + (y * z)) + (t * a)) + ((a * z) * b);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision] + N[(N[(a * z), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]

Initial Program: 92.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (+ (+ (+ x (* y z)) (* t a)) (* (* a z) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return ((x + (y * z)) + (t * a)) + ((a * z) * b);
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = ((x + (y * z)) + (t * a)) + ((a * z) * b)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return ((x + (y * z)) + (t * a)) + ((a * z) * b);
}

Python

def code(x, y, z, t, a, b):
	return ((x + (y * z)) + (t * a)) + ((a * z) * b)

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(Float64(x + Float64(y * z)) + Float64(t * a)) + Float64(Float64(a * z) * b))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = ((x + (y * z)) + (t * a)) + ((a * z) * b);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision] + N[(N[(a * z), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]

Alternative 1: 96.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z \cdot a\right) \cdot b\\ \mathbf{if}\;\left(\left(x + y \cdot z\right) + t \cdot a\right) + t_1 \leq \infty:\\ \;\;\;\;t_1 + \mathsf{fma}\left(1, x, \mathsf{fma}\left(z, y, t \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* z a) b)))
   (if (<= (+ (+ (+ x (* y z)) (* t a)) t_1) INFINITY)
     (+ t_1 (fma 1.0 x (fma z y (* t a))))
     (* a (+ t (* z b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z * a) * b;
	double tmp;
	if ((((x + (y * z)) + (t * a)) + t_1) <= ((double) INFINITY)) {
		tmp = t_1 + fma(1.0, x, fma(z, y, (t * a)));
	} else {
		tmp = a * (t + (z * b));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z * a) * b)
	tmp = 0.0
	if (Float64(Float64(Float64(x + Float64(y * z)) + Float64(t * a)) + t_1) <= Inf)
		tmp = Float64(t_1 + fma(1.0, x, fma(z, y, Float64(t * a))));
	else
		tmp = Float64(a * Float64(t + Float64(z * b)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z * a), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[N[(N[(N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], Infinity], N[(t$95$1 + N[(1.0 * x + N[(z * y + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 2: 96.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(z \cdot a\right) \cdot b\\ \mathbf{if}\;t_1 \leq \infty:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ (+ x (* y z)) (* t a)) (* (* z a) b))))
   (if (<= t_1 INFINITY) t_1 (* a (+ t (* z b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x + (y * z)) + (t * a)) + ((z * a) * b);
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = a * (t + (z * b));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x + (y * z)) + (t * a)) + ((z * a) * b);
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = a * (t + (z * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((x + (y * z)) + (t * a)) + ((z * a) * b)
	tmp = 0
	if t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = a * (t + (z * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(x + Float64(y * z)) + Float64(t * a)) + Float64(Float64(z * a) * b))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(a * Float64(t + Float64(z * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((x + (y * z)) + (t * a)) + ((z * a) * b);
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = a * (t + (z * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision] + N[(N[(z * a), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 3: 37.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.46 \cdot 10^{+180}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -4 \cdot 10^{+137}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;x \leq -6.2 \cdot 10^{+19}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{-208}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-174}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;x \leq 4 \cdot 10^{-133}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;x \leq 2.45 \cdot 10^{-39}:\\ \;\;\;\;t \cdot a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -1.46e+180)
   x
   (if (<= x -4e+137)
     (* t a)
     (if (<= x -6.2e+19)
       x
       (if (<= x 2.7e-208)
         (* y z)
         (if (<= x 8.5e-174)
           (* t a)
           (if (<= x 4e-133) (* y z) (if (<= x 2.45e-39) (* t a) x))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.46e+180) {
		tmp = x;
	} else if (x <= -4e+137) {
		tmp = t * a;
	} else if (x <= -6.2e+19) {
		tmp = x;
	} else if (x <= 2.7e-208) {
		tmp = y * z;
	} else if (x <= 8.5e-174) {
		tmp = t * a;
	} else if (x <= 4e-133) {
		tmp = y * z;
	} else if (x <= 2.45e-39) {
		tmp = t * a;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-1.46d+180)) then
        tmp = x
    else if (x <= (-4d+137)) then
        tmp = t * a
    else if (x <= (-6.2d+19)) then
        tmp = x
    else if (x <= 2.7d-208) then
        tmp = y * z
    else if (x <= 8.5d-174) then
        tmp = t * a
    else if (x <= 4d-133) then
        tmp = y * z
    else if (x <= 2.45d-39) then
        tmp = t * a
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.46e+180) {
		tmp = x;
	} else if (x <= -4e+137) {
		tmp = t * a;
	} else if (x <= -6.2e+19) {
		tmp = x;
	} else if (x <= 2.7e-208) {
		tmp = y * z;
	} else if (x <= 8.5e-174) {
		tmp = t * a;
	} else if (x <= 4e-133) {
		tmp = y * z;
	} else if (x <= 2.45e-39) {
		tmp = t * a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -1.46e+180:
		tmp = x
	elif x <= -4e+137:
		tmp = t * a
	elif x <= -6.2e+19:
		tmp = x
	elif x <= 2.7e-208:
		tmp = y * z
	elif x <= 8.5e-174:
		tmp = t * a
	elif x <= 4e-133:
		tmp = y * z
	elif x <= 2.45e-39:
		tmp = t * a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -1.46e+180)
		tmp = x;
	elseif (x <= -4e+137)
		tmp = Float64(t * a);
	elseif (x <= -6.2e+19)
		tmp = x;
	elseif (x <= 2.7e-208)
		tmp = Float64(y * z);
	elseif (x <= 8.5e-174)
		tmp = Float64(t * a);
	elseif (x <= 4e-133)
		tmp = Float64(y * z);
	elseif (x <= 2.45e-39)
		tmp = Float64(t * a);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -1.46e+180)
		tmp = x;
	elseif (x <= -4e+137)
		tmp = t * a;
	elseif (x <= -6.2e+19)
		tmp = x;
	elseif (x <= 2.7e-208)
		tmp = y * z;
	elseif (x <= 8.5e-174)
		tmp = t * a;
	elseif (x <= 4e-133)
		tmp = y * z;
	elseif (x <= 2.45e-39)
		tmp = t * a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -1.46e+180], x, If[LessEqual[x, -4e+137], N[(t * a), $MachinePrecision], If[LessEqual[x, -6.2e+19], x, If[LessEqual[x, 2.7e-208], N[(y * z), $MachinePrecision], If[LessEqual[x, 8.5e-174], N[(t * a), $MachinePrecision], If[LessEqual[x, 4e-133], N[(y * z), $MachinePrecision], If[LessEqual[x, 2.45e-39], N[(t * a), $MachinePrecision], x]]]]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 4: 38.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(z \cdot b\right)\\ \mathbf{if}\;a \leq -3.3 \cdot 10^{-17}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.9 \cdot 10^{-155}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.65 \cdot 10^{-251}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{-260}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.15 \cdot 10^{-7}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{+69}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (* z b))))
   (if (<= a -3.3e-17)
     t_1
     (if (<= a -1.9e-155)
       x
       (if (<= a -1.65e-251)
         (* y z)
         (if (<= a 1.4e-260)
           x
           (if (<= a 2.15e-7) (* y z) (if (<= a 3.6e+69) t_1 (* t a)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (z * b);
	double tmp;
	if (a <= -3.3e-17) {
		tmp = t_1;
	} else if (a <= -1.9e-155) {
		tmp = x;
	} else if (a <= -1.65e-251) {
		tmp = y * z;
	} else if (a <= 1.4e-260) {
		tmp = x;
	} else if (a <= 2.15e-7) {
		tmp = y * z;
	} else if (a <= 3.6e+69) {
		tmp = t_1;
	} else {
		tmp = t * a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (z * b)
    if (a <= (-3.3d-17)) then
        tmp = t_1
    else if (a <= (-1.9d-155)) then
        tmp = x
    else if (a <= (-1.65d-251)) then
        tmp = y * z
    else if (a <= 1.4d-260) then
        tmp = x
    else if (a <= 2.15d-7) then
        tmp = y * z
    else if (a <= 3.6d+69) then
        tmp = t_1
    else
        tmp = t * a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (z * b);
	double tmp;
	if (a <= -3.3e-17) {
		tmp = t_1;
	} else if (a <= -1.9e-155) {
		tmp = x;
	} else if (a <= -1.65e-251) {
		tmp = y * z;
	} else if (a <= 1.4e-260) {
		tmp = x;
	} else if (a <= 2.15e-7) {
		tmp = y * z;
	} else if (a <= 3.6e+69) {
		tmp = t_1;
	} else {
		tmp = t * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (z * b)
	tmp = 0
	if a <= -3.3e-17:
		tmp = t_1
	elif a <= -1.9e-155:
		tmp = x
	elif a <= -1.65e-251:
		tmp = y * z
	elif a <= 1.4e-260:
		tmp = x
	elif a <= 2.15e-7:
		tmp = y * z
	elif a <= 3.6e+69:
		tmp = t_1
	else:
		tmp = t * a
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(z * b))
	tmp = 0.0
	if (a <= -3.3e-17)
		tmp = t_1;
	elseif (a <= -1.9e-155)
		tmp = x;
	elseif (a <= -1.65e-251)
		tmp = Float64(y * z);
	elseif (a <= 1.4e-260)
		tmp = x;
	elseif (a <= 2.15e-7)
		tmp = Float64(y * z);
	elseif (a <= 3.6e+69)
		tmp = t_1;
	else
		tmp = Float64(t * a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (z * b);
	tmp = 0.0;
	if (a <= -3.3e-17)
		tmp = t_1;
	elseif (a <= -1.9e-155)
		tmp = x;
	elseif (a <= -1.65e-251)
		tmp = y * z;
	elseif (a <= 1.4e-260)
		tmp = x;
	elseif (a <= 2.15e-7)
		tmp = y * z;
	elseif (a <= 3.6e+69)
		tmp = t_1;
	else
		tmp = t * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(z * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.3e-17], t$95$1, If[LessEqual[a, -1.9e-155], x, If[LessEqual[a, -1.65e-251], N[(y * z), $MachinePrecision], If[LessEqual[a, 1.4e-260], x, If[LessEqual[a, 2.15e-7], N[(y * z), $MachinePrecision], If[LessEqual[a, 3.6e+69], t$95$1, N[(t * a), $MachinePrecision]]]]]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 5: 38.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(a \cdot b\right)\\ \mathbf{if}\;z \leq -1.35 \cdot 10^{+190}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{+61}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-289}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-86}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 10^{-29}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+111}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (* a b))))
   (if (<= z -1.35e+190)
     (* y z)
     (if (<= z -5.8e+61)
       t_1
       (if (<= z 7.5e-289)
         (* t a)
         (if (<= z 3.7e-86)
           x
           (if (<= z 1e-29) (* a (* z b)) (if (<= z 2e+111) (* y z) t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (a * b);
	double tmp;
	if (z <= -1.35e+190) {
		tmp = y * z;
	} else if (z <= -5.8e+61) {
		tmp = t_1;
	} else if (z <= 7.5e-289) {
		tmp = t * a;
	} else if (z <= 3.7e-86) {
		tmp = x;
	} else if (z <= 1e-29) {
		tmp = a * (z * b);
	} else if (z <= 2e+111) {
		tmp = y * z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (a * b)
    if (z <= (-1.35d+190)) then
        tmp = y * z
    else if (z <= (-5.8d+61)) then
        tmp = t_1
    else if (z <= 7.5d-289) then
        tmp = t * a
    else if (z <= 3.7d-86) then
        tmp = x
    else if (z <= 1d-29) then
        tmp = a * (z * b)
    else if (z <= 2d+111) then
        tmp = y * z
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (a * b);
	double tmp;
	if (z <= -1.35e+190) {
		tmp = y * z;
	} else if (z <= -5.8e+61) {
		tmp = t_1;
	} else if (z <= 7.5e-289) {
		tmp = t * a;
	} else if (z <= 3.7e-86) {
		tmp = x;
	} else if (z <= 1e-29) {
		tmp = a * (z * b);
	} else if (z <= 2e+111) {
		tmp = y * z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (a * b)
	tmp = 0
	if z <= -1.35e+190:
		tmp = y * z
	elif z <= -5.8e+61:
		tmp = t_1
	elif z <= 7.5e-289:
		tmp = t * a
	elif z <= 3.7e-86:
		tmp = x
	elif z <= 1e-29:
		tmp = a * (z * b)
	elif z <= 2e+111:
		tmp = y * z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(a * b))
	tmp = 0.0
	if (z <= -1.35e+190)
		tmp = Float64(y * z);
	elseif (z <= -5.8e+61)
		tmp = t_1;
	elseif (z <= 7.5e-289)
		tmp = Float64(t * a);
	elseif (z <= 3.7e-86)
		tmp = x;
	elseif (z <= 1e-29)
		tmp = Float64(a * Float64(z * b));
	elseif (z <= 2e+111)
		tmp = Float64(y * z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (a * b);
	tmp = 0.0;
	if (z <= -1.35e+190)
		tmp = y * z;
	elseif (z <= -5.8e+61)
		tmp = t_1;
	elseif (z <= 7.5e-289)
		tmp = t * a;
	elseif (z <= 3.7e-86)
		tmp = x;
	elseif (z <= 1e-29)
		tmp = a * (z * b);
	elseif (z <= 2e+111)
		tmp = y * z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(a * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.35e+190], N[(y * z), $MachinePrecision], If[LessEqual[z, -5.8e+61], t$95$1, If[LessEqual[z, 7.5e-289], N[(t * a), $MachinePrecision], If[LessEqual[z, 3.7e-86], x, If[LessEqual[z, 1e-29], N[(a * N[(z * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2e+111], N[(y * z), $MachinePrecision], t$95$1]]]]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 6: 86.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y \cdot z + t \cdot a\right)\\ t_2 := x + z \cdot \left(y + a \cdot b\right)\\ \mathbf{if}\;z \leq -5 \cdot 10^{+57}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-299}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-39}:\\ \;\;\;\;x + \left(t \cdot a + a \cdot \left(z \cdot b\right)\right)\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+38}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (+ (* y z) (* t a)))) (t_2 (+ x (* z (+ y (* a b))))))
   (if (<= z -5e+57)
     t_2
     (if (<= z 4e-299)
       t_1
       (if (<= z 9.5e-39)
         (+ x (+ (* t a) (* a (* z b))))
         (if (<= z 6.5e+38) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + ((y * z) + (t * a));
	double t_2 = x + (z * (y + (a * b)));
	double tmp;
	if (z <= -5e+57) {
		tmp = t_2;
	} else if (z <= 4e-299) {
		tmp = t_1;
	} else if (z <= 9.5e-39) {
		tmp = x + ((t * a) + (a * (z * b)));
	} else if (z <= 6.5e+38) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + ((y * z) + (t * a))
    t_2 = x + (z * (y + (a * b)))
    if (z <= (-5d+57)) then
        tmp = t_2
    else if (z <= 4d-299) then
        tmp = t_1
    else if (z <= 9.5d-39) then
        tmp = x + ((t * a) + (a * (z * b)))
    else if (z <= 6.5d+38) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + ((y * z) + (t * a));
	double t_2 = x + (z * (y + (a * b)));
	double tmp;
	if (z <= -5e+57) {
		tmp = t_2;
	} else if (z <= 4e-299) {
		tmp = t_1;
	} else if (z <= 9.5e-39) {
		tmp = x + ((t * a) + (a * (z * b)));
	} else if (z <= 6.5e+38) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + ((y * z) + (t * a))
	t_2 = x + (z * (y + (a * b)))
	tmp = 0
	if z <= -5e+57:
		tmp = t_2
	elif z <= 4e-299:
		tmp = t_1
	elif z <= 9.5e-39:
		tmp = x + ((t * a) + (a * (z * b)))
	elif z <= 6.5e+38:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(Float64(y * z) + Float64(t * a)))
	t_2 = Float64(x + Float64(z * Float64(y + Float64(a * b))))
	tmp = 0.0
	if (z <= -5e+57)
		tmp = t_2;
	elseif (z <= 4e-299)
		tmp = t_1;
	elseif (z <= 9.5e-39)
		tmp = Float64(x + Float64(Float64(t * a) + Float64(a * Float64(z * b))));
	elseif (z <= 6.5e+38)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + ((y * z) + (t * a));
	t_2 = x + (z * (y + (a * b)));
	tmp = 0.0;
	if (z <= -5e+57)
		tmp = t_2;
	elseif (z <= 4e-299)
		tmp = t_1;
	elseif (z <= 9.5e-39)
		tmp = x + ((t * a) + (a * (z * b)));
	elseif (z <= 6.5e+38)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(N[(y * z), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(z * N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5e+57], t$95$2, If[LessEqual[z, 4e-299], t$95$1, If[LessEqual[z, 9.5e-39], N[(x + N[(N[(t * a), $MachinePrecision] + N[(a * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.5e+38], t$95$1, t$95$2]]]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 7: 86.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y \cdot z + t \cdot a\right)\\ t_2 := x + z \cdot \left(y + a \cdot b\right)\\ \mathbf{if}\;z \leq -2.3 \cdot 10^{+60}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-86}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-38}:\\ \;\;\;\;y \cdot z + a \cdot \left(t + z \cdot b\right)\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+38}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (+ (* y z) (* t a)))) (t_2 (+ x (* z (+ y (* a b))))))
   (if (<= z -2.3e+60)
     t_2
     (if (<= z 1.9e-86)
       t_1
       (if (<= z 6.2e-38)
         (+ (* y z) (* a (+ t (* z b))))
         (if (<= z 9.5e+38) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + ((y * z) + (t * a));
	double t_2 = x + (z * (y + (a * b)));
	double tmp;
	if (z <= -2.3e+60) {
		tmp = t_2;
	} else if (z <= 1.9e-86) {
		tmp = t_1;
	} else if (z <= 6.2e-38) {
		tmp = (y * z) + (a * (t + (z * b)));
	} else if (z <= 9.5e+38) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + ((y * z) + (t * a))
    t_2 = x + (z * (y + (a * b)))
    if (z <= (-2.3d+60)) then
        tmp = t_2
    else if (z <= 1.9d-86) then
        tmp = t_1
    else if (z <= 6.2d-38) then
        tmp = (y * z) + (a * (t + (z * b)))
    else if (z <= 9.5d+38) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + ((y * z) + (t * a));
	double t_2 = x + (z * (y + (a * b)));
	double tmp;
	if (z <= -2.3e+60) {
		tmp = t_2;
	} else if (z <= 1.9e-86) {
		tmp = t_1;
	} else if (z <= 6.2e-38) {
		tmp = (y * z) + (a * (t + (z * b)));
	} else if (z <= 9.5e+38) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + ((y * z) + (t * a))
	t_2 = x + (z * (y + (a * b)))
	tmp = 0
	if z <= -2.3e+60:
		tmp = t_2
	elif z <= 1.9e-86:
		tmp = t_1
	elif z <= 6.2e-38:
		tmp = (y * z) + (a * (t + (z * b)))
	elif z <= 9.5e+38:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(Float64(y * z) + Float64(t * a)))
	t_2 = Float64(x + Float64(z * Float64(y + Float64(a * b))))
	tmp = 0.0
	if (z <= -2.3e+60)
		tmp = t_2;
	elseif (z <= 1.9e-86)
		tmp = t_1;
	elseif (z <= 6.2e-38)
		tmp = Float64(Float64(y * z) + Float64(a * Float64(t + Float64(z * b))));
	elseif (z <= 9.5e+38)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + ((y * z) + (t * a));
	t_2 = x + (z * (y + (a * b)));
	tmp = 0.0;
	if (z <= -2.3e+60)
		tmp = t_2;
	elseif (z <= 1.9e-86)
		tmp = t_1;
	elseif (z <= 6.2e-38)
		tmp = (y * z) + (a * (t + (z * b)));
	elseif (z <= 9.5e+38)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(N[(y * z), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(z * N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.3e+60], t$95$2, If[LessEqual[z, 1.9e-86], t$95$1, If[LessEqual[z, 6.2e-38], N[(N[(y * z), $MachinePrecision] + N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.5e+38], t$95$1, t$95$2]]]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 8: 93.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 6.2 \cdot 10^{+147}:\\ \;\;\;\;\left(x + y \cdot z\right) + \left(t \cdot a + a \cdot \left(z \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(y + a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z 6.2e+147)
   (+ (+ x (* y z)) (+ (* t a) (* a (* z b))))
   (+ x (* z (+ y (* a b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= 6.2e+147) {
		tmp = (x + (y * z)) + ((t * a) + (a * (z * b)));
	} else {
		tmp = x + (z * (y + (a * b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= 6.2d+147) then
        tmp = (x + (y * z)) + ((t * a) + (a * (z * b)))
    else
        tmp = x + (z * (y + (a * b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= 6.2e+147) {
		tmp = (x + (y * z)) + ((t * a) + (a * (z * b)));
	} else {
		tmp = x + (z * (y + (a * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= 6.2e+147:
		tmp = (x + (y * z)) + ((t * a) + (a * (z * b)))
	else:
		tmp = x + (z * (y + (a * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= 6.2e+147)
		tmp = Float64(Float64(x + Float64(y * z)) + Float64(Float64(t * a) + Float64(a * Float64(z * b))));
	else
		tmp = Float64(x + Float64(z * Float64(y + Float64(a * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= 6.2e+147)
		tmp = (x + (y * z)) + ((t * a) + (a * (z * b)));
	else
		tmp = x + (z * (y + (a * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, 6.2e+147], N[(N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(N[(t * a), $MachinePrecision] + N[(a * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 9: 73.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + t \cdot a\\ t_2 := z \cdot \left(y + a \cdot b\right)\\ \mathbf{if}\;z \leq -1.4 \cdot 10^{+36}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-86}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-23}:\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+45}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* t a))) (t_2 (* z (+ y (* a b)))))
   (if (<= z -1.4e+36)
     t_2
     (if (<= z 4.6e-86)
       t_1
       (if (<= z 4.5e-23) (* a (+ t (* z b))) (if (<= z 1.7e+45) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (t * a);
	double t_2 = z * (y + (a * b));
	double tmp;
	if (z <= -1.4e+36) {
		tmp = t_2;
	} else if (z <= 4.6e-86) {
		tmp = t_1;
	} else if (z <= 4.5e-23) {
		tmp = a * (t + (z * b));
	} else if (z <= 1.7e+45) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (t * a)
    t_2 = z * (y + (a * b))
    if (z <= (-1.4d+36)) then
        tmp = t_2
    else if (z <= 4.6d-86) then
        tmp = t_1
    else if (z <= 4.5d-23) then
        tmp = a * (t + (z * b))
    else if (z <= 1.7d+45) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (t * a);
	double t_2 = z * (y + (a * b));
	double tmp;
	if (z <= -1.4e+36) {
		tmp = t_2;
	} else if (z <= 4.6e-86) {
		tmp = t_1;
	} else if (z <= 4.5e-23) {
		tmp = a * (t + (z * b));
	} else if (z <= 1.7e+45) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (t * a)
	t_2 = z * (y + (a * b))
	tmp = 0
	if z <= -1.4e+36:
		tmp = t_2
	elif z <= 4.6e-86:
		tmp = t_1
	elif z <= 4.5e-23:
		tmp = a * (t + (z * b))
	elif z <= 1.7e+45:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(t * a))
	t_2 = Float64(z * Float64(y + Float64(a * b)))
	tmp = 0.0
	if (z <= -1.4e+36)
		tmp = t_2;
	elseif (z <= 4.6e-86)
		tmp = t_1;
	elseif (z <= 4.5e-23)
		tmp = Float64(a * Float64(t + Float64(z * b)));
	elseif (z <= 1.7e+45)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (t * a);
	t_2 = z * (y + (a * b));
	tmp = 0.0;
	if (z <= -1.4e+36)
		tmp = t_2;
	elseif (z <= 4.6e-86)
		tmp = t_1;
	elseif (z <= 4.5e-23)
		tmp = a * (t + (z * b));
	elseif (z <= 1.7e+45)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(t * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.4e+36], t$95$2, If[LessEqual[z, 4.6e-86], t$95$1, If[LessEqual[z, 4.5e-23], N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.7e+45], t$95$1, t$95$2]]]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 10: 82.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+63} \lor \neg \left(z \leq 3.7 \cdot 10^{+49}\right):\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot z + t \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.45e+63) (not (<= z 3.7e+49)))
   (* z (+ y (* a b)))
   (+ x (+ (* y z) (* t a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.45e+63) || !(z <= 3.7e+49)) {
		tmp = z * (y + (a * b));
	} else {
		tmp = x + ((y * z) + (t * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-1.45d+63)) .or. (.not. (z <= 3.7d+49))) then
        tmp = z * (y + (a * b))
    else
        tmp = x + ((y * z) + (t * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.45e+63) || !(z <= 3.7e+49)) {
		tmp = z * (y + (a * b));
	} else {
		tmp = x + ((y * z) + (t * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.45e+63) or not (z <= 3.7e+49):
		tmp = z * (y + (a * b))
	else:
		tmp = x + ((y * z) + (t * a))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.45e+63) || !(z <= 3.7e+49))
		tmp = Float64(z * Float64(y + Float64(a * b)));
	else
		tmp = Float64(x + Float64(Float64(y * z) + Float64(t * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1.45e+63) || ~((z <= 3.7e+49)))
		tmp = z * (y + (a * b));
	else
		tmp = x + ((y * z) + (t * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.45e+63], N[Not[LessEqual[z, 3.7e+49]], $MachinePrecision]], N[(z * N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * z), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 11: 86.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{+56} \lor \neg \left(z \leq 1.7 \cdot 10^{+39}\right):\\ \;\;\;\;x + z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot z + t \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -6.6e+56) (not (<= z 1.7e+39)))
   (+ x (* z (+ y (* a b))))
   (+ x (+ (* y z) (* t a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -6.6e+56) || !(z <= 1.7e+39)) {
		tmp = x + (z * (y + (a * b)));
	} else {
		tmp = x + ((y * z) + (t * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-6.6d+56)) .or. (.not. (z <= 1.7d+39))) then
        tmp = x + (z * (y + (a * b)))
    else
        tmp = x + ((y * z) + (t * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -6.6e+56) || !(z <= 1.7e+39)) {
		tmp = x + (z * (y + (a * b)));
	} else {
		tmp = x + ((y * z) + (t * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -6.6e+56) or not (z <= 1.7e+39):
		tmp = x + (z * (y + (a * b)))
	else:
		tmp = x + ((y * z) + (t * a))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -6.6e+56) || !(z <= 1.7e+39))
		tmp = Float64(x + Float64(z * Float64(y + Float64(a * b))));
	else
		tmp = Float64(x + Float64(Float64(y * z) + Float64(t * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -6.6e+56) || ~((z <= 1.7e+39)))
		tmp = x + (z * (y + (a * b)));
	else
		tmp = x + ((y * z) + (t * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -6.6e+56], N[Not[LessEqual[z, 1.7e+39]], $MachinePrecision]], N[(x + N[(z * N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * z), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 12: 74.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.2 \cdot 10^{-16} \lor \neg \left(a \leq 2.7 \cdot 10^{+37}\right):\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -1.2e-16) (not (<= a 2.7e+37)))
   (* a (+ t (* z b)))
   (+ x (* y z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -1.2e-16) || !(a <= 2.7e+37)) {
		tmp = a * (t + (z * b));
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((a <= (-1.2d-16)) .or. (.not. (a <= 2.7d+37))) then
        tmp = a * (t + (z * b))
    else
        tmp = x + (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -1.2e-16) || !(a <= 2.7e+37)) {
		tmp = a * (t + (z * b));
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -1.2e-16) or not (a <= 2.7e+37):
		tmp = a * (t + (z * b))
	else:
		tmp = x + (y * z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -1.2e-16) || !(a <= 2.7e+37))
		tmp = Float64(a * Float64(t + Float64(z * b)));
	else
		tmp = Float64(x + Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -1.2e-16) || ~((a <= 2.7e+37)))
		tmp = a * (t + (z * b));
	else
		tmp = x + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -1.2e-16], N[Not[LessEqual[a, 2.7e+37]], $MachinePrecision]], N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 13: 57.1% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.08 \cdot 10^{-16}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{+79}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -1.08e-16) (* a (* z b)) (if (<= a 2.2e+79) (+ x (* y z)) (* t a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -1.08e-16) {
		tmp = a * (z * b);
	} else if (a <= 2.2e+79) {
		tmp = x + (y * z);
	} else {
		tmp = t * a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-1.08d-16)) then
        tmp = a * (z * b)
    else if (a <= 2.2d+79) then
        tmp = x + (y * z)
    else
        tmp = t * a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -1.08e-16) {
		tmp = a * (z * b);
	} else if (a <= 2.2e+79) {
		tmp = x + (y * z);
	} else {
		tmp = t * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -1.08e-16:
		tmp = a * (z * b)
	elif a <= 2.2e+79:
		tmp = x + (y * z)
	else:
		tmp = t * a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -1.08e-16)
		tmp = Float64(a * Float64(z * b));
	elseif (a <= 2.2e+79)
		tmp = Float64(x + Float64(y * z));
	else
		tmp = Float64(t * a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -1.08e-16)
		tmp = a * (z * b);
	elseif (a <= 2.2e+79)
		tmp = x + (y * z);
	else
		tmp = t * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -1.08e-16], N[(a * N[(z * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.2e+79], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision], N[(t * a), $MachinePrecision]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 14: 59.4% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.35 \cdot 10^{-16}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;a \leq 7 \cdot 10^{+71}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -1.35e-16)
   (* a (* z b))
   (if (<= a 7e+71) (+ x (* y z)) (+ x (* t a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -1.35e-16) {
		tmp = a * (z * b);
	} else if (a <= 7e+71) {
		tmp = x + (y * z);
	} else {
		tmp = x + (t * a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-1.35d-16)) then
        tmp = a * (z * b)
    else if (a <= 7d+71) then
        tmp = x + (y * z)
    else
        tmp = x + (t * a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -1.35e-16) {
		tmp = a * (z * b);
	} else if (a <= 7e+71) {
		tmp = x + (y * z);
	} else {
		tmp = x + (t * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -1.35e-16:
		tmp = a * (z * b)
	elif a <= 7e+71:
		tmp = x + (y * z)
	else:
		tmp = x + (t * a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -1.35e-16)
		tmp = Float64(a * Float64(z * b));
	elseif (a <= 7e+71)
		tmp = Float64(x + Float64(y * z));
	else
		tmp = Float64(x + Float64(t * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -1.35e-16)
		tmp = a * (z * b);
	elseif (a <= 7e+71)
		tmp = x + (y * z);
	else
		tmp = x + (t * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -1.35e-16], N[(a * N[(z * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7e+71], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * a), $MachinePrecision]), $MachinePrecision]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 15: 39.0% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{+20} \lor \neg \left(t \leq 5.4 \cdot 10^{+100}\right):\\ \;\;\;\;t \cdot a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -4e+20) (not (<= t 5.4e+100))) (* t a) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -4e+20) || !(t <= 5.4e+100)) {
		tmp = t * a;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-4d+20)) .or. (.not. (t <= 5.4d+100))) then
        tmp = t * a
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -4e+20) || !(t <= 5.4e+100)) {
		tmp = t * a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -4e+20) or not (t <= 5.4e+100):
		tmp = t * a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -4e+20) || !(t <= 5.4e+100))
		tmp = Float64(t * a);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -4e+20) || ~((t <= 5.4e+100)))
		tmp = t * a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -4e+20], N[Not[LessEqual[t, 5.4e+100]], $MachinePrecision]], N[(t * a), $MachinePrecision], x]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 16: 26.2% accurate, 15.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 x)

C

double code(double x, double y, double z, double t, double a, double b) {
	return x;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = x
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return x;
}

Python

def code(x, y, z, t, a, b):
	return x

Julia

function code(x, y, z, t, a, b)
	return x
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = x;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := x

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Developer target: 97.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(b \cdot a + y\right) + \left(x + t \cdot a\right)\\ \mathbf{if}\;z < -11820553527347888000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z < 4.7589743188364287 \cdot 10^{-122}:\\ \;\;\;\;\left(b \cdot z + t\right) \cdot a + \left(z \cdot y + x\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (* z (+ (* b a) y)) (+ x (* t a)))))
   (if (< z -11820553527347888000.0)
     t_1
     (if (< z 4.7589743188364287e-122)
       (+ (* (+ (* b z) t) a) (+ (* z y) x))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z * ((b * a) + y)) + (x + (t * a));
	double tmp;
	if (z < -11820553527347888000.0) {
		tmp = t_1;
	} else if (z < 4.7589743188364287e-122) {
		tmp = (((b * z) + t) * a) + ((z * y) + x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z * ((b * a) + y)) + (x + (t * a))
    if (z < (-11820553527347888000.0d0)) then
        tmp = t_1
    else if (z < 4.7589743188364287d-122) then
        tmp = (((b * z) + t) * a) + ((z * y) + x)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z * ((b * a) + y)) + (x + (t * a));
	double tmp;
	if (z < -11820553527347888000.0) {
		tmp = t_1;
	} else if (z < 4.7589743188364287e-122) {
		tmp = (((b * z) + t) * a) + ((z * y) + x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z * ((b * a) + y)) + (x + (t * a))
	tmp = 0
	if z < -11820553527347888000.0:
		tmp = t_1
	elif z < 4.7589743188364287e-122:
		tmp = (((b * z) + t) * a) + ((z * y) + x)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z * Float64(Float64(b * a) + y)) + Float64(x + Float64(t * a)))
	tmp = 0.0
	if (z < -11820553527347888000.0)
		tmp = t_1;
	elseif (z < 4.7589743188364287e-122)
		tmp = Float64(Float64(Float64(Float64(b * z) + t) * a) + Float64(Float64(z * y) + x));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z * ((b * a) + y)) + (x + (t * a));
	tmp = 0.0;
	if (z < -11820553527347888000.0)
		tmp = t_1;
	elseif (z < 4.7589743188364287e-122)
		tmp = (((b * z) + t) * a) + ((z * y) + x);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z * N[(N[(b * a), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision] + N[(x + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[z, -11820553527347888000.0], t$95$1, If[Less[z, 4.7589743188364287e-122], N[(N[(N[(N[(b * z), $MachinePrecision] + t), $MachinePrecision] * a), $MachinePrecision] + N[(N[(z * y), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2024010 
(FPCore (x y z t a b)
  :name "Graphics.Rasterific.CubicBezier:cachedBezierAt from Rasterific-0.6.1"
  :precision binary64

  :herbie-target
  (if (< z -11820553527347888000.0) (+ (* z (+ (* b a) y)) (+ x (* t a))) (if (< z 4.7589743188364287e-122) (+ (* (+ (* b z) t) a) (+ (* z y) x)) (+ (* z (+ (* b a) y)) (+ x (* t a)))))

  (+ (+ (+ x (* y z)) (* t a)) (* (* a z) b)))